Course: 2024/2025

Applied differential calculus

(15975)

Requirements (Subjects that are assumed to be known)

Calculus (Course 1 - Semester 1)
Linear Algebra (Course 1 - Semester 1)

The objective of the course is to provide the student with the necessary tools to understand the scientific and mathematical principles of computer engineering.

Skills and learning outcomes

Description of contents: programme

1.- First order differential equations:
a. Introduction.
b. Separable equations.
c. Linear equations.
d. Exact equations.
e. Homogeneous equations.
2.- Second order differential equations.
a. Linear and nonlinear equations.
b. Homogeneous and non-homogeneous linear Equations.
c. Reduction of order.
d. Euler-Cauchy equations.
3.- The Laplace Transform:
a. Definition. Properties.
b. Application to differential equations.
4.- Systems of differential equations:
a. Linear and nonlinear systems.
b. Vectorial representation.
c. Eigenvalues and linearization.
5. Fourier series and separation of variables:
a. Basic results.
b. Fourier Sine and Cosine Series.
c. Applications of Fourier series and separation of variables to partial differential equations.
6.- Numerical methods:
a. Euler method.
b. Runge-Kutta method.
c. Boundary value problems.

Learning activities and methodology

1.- Teaching in big or aggregate groups. Lectures sessions (3 ECTS).
2.- Face-to-face teaching in small groups. Problem sessions with individual and group work (3 ECTS).
Office hours: Each teacher offers a number of office hours according to the regulations of the Carlos III University. In particular, a minimum of one hour per group with the time schedule compatible with the students.

Assessment System

- % end-of-term-examination 60
- % of continuous assessment (assigments, laboratory, practicals...) 40

Calendar of Continuous assessment

Extraordinary call: regulations

Basic Bibliography

- Boyce, William E.. Elementary differential equations and boundary value problems . John Wiley & Sons,.
- Simmons, George Finlay. Differential equations with applications and historical notes.. McGraw-Hill.
- Zill, Dennis G.. Ecuaciones diferenciales con aplicaciones de modelado . International Thomson.

- Manuel Carretero, Luis L. Bonilla, Filippo Terragni, Segei Iakunin, Rocío Vega · Curse OCW-UC3M Applied Differential Calculus : http://ocw.uc3m.es/matematicas/applied-differential-calculus

Additional Bibliography

- Haberman, Richard . Elementary applied partial differential equations with Fourier series and boundary value problems 3rd ed. Prentice Hall.
- Gockenbach, Mark S.. Partial differential equations : analytical and numerical methods. SIAM.
- Kiseliov, Aleksandr I.. Problemas de ecuaciones diferenciales ordinarias . Mir.
- Weinberger, Hans F. . A first course in partial differential equations with complex variables and transform methods. Dover.

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The course syllabus may change due academic events or other reasons.